Display the Math Practices page where all students can see it.
Gather small and larger containers for water. See Lessons 3 and 4 Materials Preparation.
Gather collections of small objects that sink and float. See Lesson 3 Materials Preparation.
Organize two-pan balances with sets of gram masses. See Lessons 3 and 4 Materials Preparation.
Gather steel spheres in different sizes. See Lesson 4 Materials Preparation.
Gather string that does not stretch for Lesson 5.
Collect circular objects (e.g., cans, lids) of various sizes for Lesson 5.
Gather resealable bags and several 1-pound packages of small beans. See Lesson 6 Materials Preparation.
Have the following tools readily available for the Daily Practice and Problems items in this unit:
Students will need:
- centimeter rulers
- calculators
- rulers
- Centimeter Grid Paper
(Teacher Guide) - Reference section (Student Guide)
You will also need a prepared set of Digit Cards 0–9 (Teacher Guide)
| LESSON | SESSIONS | DESCRIPTION | SUPPLIES |
|---|---|---|---|
LESSON 1Ratios, Recipes, and Proportions |
2–3 | Students use recipes as a context to learn about ratios using tables, graphs and fractions. Students write ratios as fractions and use colon notation. A proportion is defined as A statement indicating that two ratios are equal. Students then use proportions and strategies for finding equivalent fractions to solve problems. |
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LESSON 2Variables in Proportion |
2–3 | Students investigate the concept of proportion as it applies to variables in experiments. Students use strategies for finding equivalent ratios and proportions to solve problems. |
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LESSON 3Sink and Float |
3 | Students find the mass and volume for several objects and observe which objects sink and which objects float in water. Students discover how the ratio of mass to volume predicts whether an object will sink or float. |
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LESSON 4Mass vs. Volume: Proportions and Density |
4–5 | Students find the mass and volume of different amounts of clay and different-sized steel spheres. They use proportional reasoning to discover that the density of a material does not change when different amounts of a material are measured. Several extension activites are offered following the lesson. |
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LESSON 5Explore Circumference and Diameter |
4 | Students explore the relationship between the circumference and the diameter of circles, record their measurements in a data table, plot them on a graph, and analyze their results. Students find that the circumference of a circle is about three times its diameter and equal to π times the diameter. |
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LESSON 6Sampling and Proportion |
4 | Students read the story “Bats” and use connections between ratios, proportions, and graphing to determine whether the number of tagged bats (t) in a fictional sample is proportional to the total number of bats (n) in the sample. Students then simulate this story with a lab investigation of their own using beans in a container to represent bats in a cave. Students use sampling ratios, graphs, and proportional reasoning to find an approximation of the total number of bats in their cave. |
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LESSON 7End-of-Year Test |
1–2 | Students take a paper-and-pencil test that assesses skills and concepts studied in the last five units. |
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